We develop an untyped semantic framework for the multiverse of set theory and show that its proof-theoretic commitments are mild. ZF is extended with semantical axioms utilizing the new symbols M(U) and M(U,σ), expressing that U is a universe and that σ is true in the universe U, respectively. Here σ ranges over the augmented language, leading to liar-style phenomena that are analysed. The framework is both compatible with a broad range of multiverse conceptions and suggests its own philosophically and semantically motivated multiverse principles.